Advertisements

Neural Darwinism made simple

Forget all those technical treatises on the evolution of neuronal topology. Here’s all you need to know:

“Well you see, Norm, it’s like this… A herd of buffalo can only move as fast as the slowest buffalo. And when the herd is hunted, it is the slowest and weakest ones at the back that are killed first. This natural selection is good for the herd as a whole, because the general speed and health of the whole group keeps improving by the regular killing of the weakest members. In much the same way, the human brain can only operate as fast as the slowest brain cells. Now, as we know, excessive intake of alcohol kills brain cells. But naturally, it attacks the slowest and weakest brain cells first. In this way, regular consumption of beer eliminates the weaker brain cells, making the brain a faster and more efficient machine. And that, Norm, is why you always feel smarter after a few beers.”

I suppose we do agree here. Now, we look at a search Φ as a Ωm-valued random variable, i.e., Φ := (φ1, φ2, …, , φm).

When is it successful? If we are still looking for a T ⊆ Ω we can say that we found T during our search if

Φ ∈ Ωm / (Ω / T)m

Let’s define Θ as the subspace of Ωm which exists from the representations of targets in Ω, i.e.,

Θ := {Ωm / (Ω / T)m|T non-empty subset Ω}

Obviously, Θ is much smaller than Ωm.

But this Θ is the space of feasible targets. And if you take an exhaustive partition of Θ instead of Ω in Theorem III.1 Horizontal No Free Lunch, you’ll find that you can indeed have positive values for the active entropy as defined in the same theorem.

But that’s not much of a surprise, as random sampling without repetition works better than random sampling with repetition.

But if you allow T to be any subset of Ωm, your resutls get somewhat trivial, as you are now looking at m independent searches of length 1 for different targets.

The searches which you state as examples in this paper and the previous one all work with a fixed target, i.e., elements of Θ. You never mention the possibility that the target changes between the steps of the search (one possible interpretation of taking arbitrary sets of Ωm> into account).

So, I’m faced with to possibilities:You didn’t realize the switch from stationary targets to moving ones when you introduced searching for an arbitary subset of ΩmYou realized this switch to a very different concept, but chose not to stress the point.

“Thanks Cliff!” says Woody. “You know Mr Peterson, it’s a good thing these dying weaker brain cells don’t hold any important adaptive information such as your social security number. And why is it that dying brain cells never kill your beliefs that keep you from rationally reasoning and scientifically theorizing about women and beer? Can I pour you a beer Mr. Peterson?”
“A little early isn’t it, Woody?”
“For a beer?”
“No, for stupid questions.”